For example, a device based on a method of Ho-Kalman is disclosed in Non Patent Literature 1 as a conventional system identification device using an impulse response. In this method, a direct feedthrough term Dd of a system is determined from G0, and a block Hankel matrix Hkl is generated from G1, G2, . . . based on an impulse response (G0, G1, G2, . . . ) of a dynamic system delineated by a linear discrete-time system (Ad, Bd, Cd, Dd). Subsequently, singular value decomposition is applied to the block Hankel matrix Hkl, the number of singular values having significant values is determined to be a system dimension, and an extended observability matrix Ok and an extended reachability matrix Cl are calculated from the determined system dimension and a result of singular value decomposition. Finally, the linear discrete-time system (Ad, Bd, Cd, Dd) that delineates the dynamic system is identified by calculating system matrices Ad, Bd, and Cd based on the extended observability matrix Ok and the extended reachability matrix Cl.
In addition, for example, a plant modeling device is disclosed in Patent Literature 1 as another example of a conventional system identification device using an impulse response. In this plant modeling device, the above-described method of Ho-Kalman is applied to an impulse response (G0, G1, G2, . . . ) of a dynamic system. However, two types of methods below are selectively applied as a method of determining a system dimension. A first system dimension determination method is a method of displaying a relation between a singular value and a degree corresponding to the singular value in a logarithmic scale on a graphic terminal, and determining the number of singular values having significant values, that is, a system dimension by an operator. A second system dimension determination method is a method of applying an evaluation function based on a rate of change of a singular value and observation noise, and automatically determining a dimension, at which the evaluation function is the smallest, to be a system dimension.
In such a system identification device using an impulse response, a system dimension is determined from the number of singular values having significant values.